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Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type > Class Template Reference

Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...

#include <Stokhos_ProductLanczosPCEBasis.hpp>

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Public Member Functions

 ProductLanczosPCEBasis (ordinal_type p, const Teuchos::Array< Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &pce, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad, const Teuchos::RCP< const Stokhos::Sparse3Tensor< ordinal_type, value_type > > &Cijk, const Teuchos::ParameterList &params=Teuchos::ParameterList())
 Constructor. More...
 
virtual ~ProductLanczosPCEBasis ()
 Destructor.
 
Implementation of Stokhos::OrthogPolyBasis methods
ordinal_type order () const
 Return order of basis.
 
ordinal_type dimension () const
 Return dimension of basis.
 
virtual ordinal_type size () const
 Return total size of basis.
 
virtual const Teuchos::Array
< value_type > & 
norm_squared () const
 Return array storing norm-squared of each basis polynomial. More...
 
virtual const value_type & norm_squared (ordinal_type i) const
 Return norm squared of basis polynomial i.
 
virtual Teuchos::RCP
< Stokhos::Sparse3Tensor
< ordinal_type, value_type > > 
computeTripleProductTensor () const
 Compute triple product tensor. More...
 
virtual Teuchos::RCP
< Stokhos::Sparse3Tensor
< ordinal_type, value_type > > 
computeLinearTripleProductTensor () const
 Compute linear triple product tensor where k = 0,1,..,d.
 
virtual value_type evaluateZero (ordinal_type i) const
 Evaluate basis polynomial i at zero.
 
virtual void evaluateBases (const Teuchos::ArrayView< const value_type > &point, Teuchos::Array< value_type > &basis_vals) const
 Evaluate basis polynomials at given point point. More...
 
virtual void print (std::ostream &os) const
 Print basis to stream os.
 
virtual const std::string & getName () const
 Return string name of basis.
 
Implementation of Stokhos::ProductBasis methods
virtual const MultiIndex
< ordinal_type > & 
term (ordinal_type i) const
 Get orders of each coordinate polynomial given an index i. More...
 
virtual ordinal_type index (const MultiIndex< ordinal_type > &term) const
 Get index of the multivariate polynomial given orders of each coordinate. More...
 
Teuchos::Array< Teuchos::RCP
< const OneDOrthogPolyBasis
< ordinal_type, value_type > > > 
getCoordinateBases () const
 Return coordinate bases. More...
 
virtual MultiIndex< ordinal_type > getMaxOrders () const
 Return maximum order allowable for each coordinate basis.
 
Implementation of Stokhos::ReducedPCEBasis methods
virtual void transformToOriginalBasis (const value_type *in, value_type *out, ordinal_type ncol=1, bool transpose=false) const
 Transform coefficients to original basis from this basis.
 
virtual void transformFromOriginalBasis (const value_type *in, value_type *out, ordinal_type ncol=1, bool transpose=false) const
 Transform coefficients from original basis to this basis.
 
virtual Teuchos::RCP< const
Stokhos::Quadrature
< ordinal_type, value_type > > 
getReducedQuadrature () const
 Get reduced quadrature object.
 
- Public Member Functions inherited from Stokhos::ProductBasis< ordinal_type, value_type >
 ProductBasis ()
 Constructor.
 
virtual ~ProductBasis ()
 Destructor.
 
- Public Member Functions inherited from Stokhos::OrthogPolyBasis< ordinal_type, value_type >
 OrthogPolyBasis ()
 Constructor.
 
virtual ~OrthogPolyBasis ()
 Destructor.
 
- Public Member Functions inherited from Stokhos::ReducedPCEBasis< ordinal_type, value_type >
 ReducedPCEBasis ()
 Default constructor.
 
virtual ~ReducedPCEBasis ()
 Destructor.
 

Protected Types

typedef
Teuchos::SerialDenseVector
< ordinal_type, value_type > 
SDV
 
typedef
Teuchos::SerialDenseMatrix
< ordinal_type, value_type > 
SDM
 

Protected Member Functions

ordinal_type isInvariant (const Stokhos::OrthogPolyApprox< ordinal_type, value_type > &pce) const
 

Protected Attributes

std::string name
 Name of basis.
 
Teuchos::ParameterList params
 Algorithm parameters.
 
Teuchos::RCP
< Stokhos::CompletePolynomialBasis
< ordinal_type, value_type > > 
tensor_lanczos_basis
 Product Lanczos basis.
 
SDM Phi
 Values of transformed basis at quadrature points.
 
SDM A
 Transition matrix from reduced basis to original.
 
SDM Ainv
 Projection matrix from original matrix to reduced.
 
Teuchos::RCP< const
Stokhos::Quadrature
< ordinal_type, value_type > > 
reduced_quad
 Reduced quadrature object.
 
Stokhos::OrthogPolyApprox
< ordinal_type, value_type > 
tmp_pce
 Temporary pce used in invariant subspace calculations.
 

Detailed Description

template<typename ordinal_type, typename value_type>
class Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >

Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions.

Given the PCE expansions, first build a an orthogonal basis for each compnent, then form the multivariate basis by a total-order tensor product. The resulting basis is not necessarily orthogonal with respect to the full measure.

Constructor & Destructor Documentation

template<typename ordinal_type , typename value_type >
Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::ProductLanczosPCEBasis ( ordinal_type  p,
const Teuchos::Array< Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &  pce,
const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &  quad,
const Teuchos::RCP< const Stokhos::Sparse3Tensor< ordinal_type, value_type > > &  Cijk,
const Teuchos::ParameterList &  params = Teuchos::ParameterList() 
)

Member Function Documentation

template<typename ordinal_type , typename value_type >
Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::computeTripleProductTensor ( ) const
virtual

Compute triple product tensor.

The $(i,j,k)$ entry of the tensor $C_{ijk}$ is given by $C_{ijk} = \langle\Psi_i\Psi_j\Psi_k\rangle$ where $\Psi_l$ represents basis polynomial $l$ and $i,j,k=0,\dots,P$ where $P$ is size()-1.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >
void Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::evaluateBases ( const Teuchos::ArrayView< const value_type > &  point,
Teuchos::Array< value_type > &  basis_vals 
) const
virtual

Evaluate basis polynomials at given point point.

Size of returned array is given by size(), and coefficients are ordered from order 0 up to size size()-1.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >
Teuchos::Array< Teuchos::RCP< const Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type > > > Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::getCoordinateBases ( ) const
virtual

Return coordinate bases.

Array is of size dimension().

Implements Stokhos::ProductBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::index ( const MultiIndex< ordinal_type > &  term) const
virtual

Get index of the multivariate polynomial given orders of each coordinate.

Given the array term storing $i_1,\dots,\i_d$, returns the index $i$ such that $\Psi_i(x) = \psi_{i_1}(x_1)\dots\psi_{i_d}(x_d)$.

Implements Stokhos::ProductBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >
const Teuchos::Array< value_type > & Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::norm_squared ( ) const
virtual

Return array storing norm-squared of each basis polynomial.

Entry $l$ of returned array is given by $\langle\Psi_l^2\rangle$ for $l=0,\dots,P$ where $P$ is size()-1.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >
const Stokhos::MultiIndex< ordinal_type > & Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::term ( ordinal_type  i) const
virtual

Get orders of each coordinate polynomial given an index i.

The returned array is of size $d$, where $d$ is the dimension of the basis, and entry $l$ is given by $i_l$ where $\Psi_i(x) = \psi_{i_1}(x_1)\dots\psi_{i_d}(x_d)$.

Implements Stokhos::ProductBasis< ordinal_type, value_type >.


The documentation for this class was generated from the following files: